For $|t|$ sufficiently small, the Calabi-Yau metrics $\omega_{CY,t}$ on $X_{t}$ can be constructed by gluing the Tian-Yau metrics on $Y_{1}\setminus D$ and $Y_{2}\setminus D$, together with an approximately Calabi-Yau metric on a transition region. We normalize $\omega_{CY,t}$ so that $\diam(X_{t},{\omega_{CY,t}})=1$, and we denote by $d\underline{\nu}_{t}$ the renormalized measure of $(X_{t},\omega_{CY,t})$. Then the following holds as $t\to 0$ (see Figure 1.2):

1. (1)

   Under measured Gromov-Hausdorff convergence, the spaces collapse to the unit interval with a singular renormalized limit measure, that is,

   (1.2)

   $$(X_{t},\omega_{CY,t},d\underline{\nu}_{t})\xrightarrow{mGH}(\mathbb{I},dv^{2},d\underline{\nu}_{\mathbb{I}}),$$

   where $\mathbb{I}=[-\frac{d_{1}}{d_{1}+d_{2}},\frac{d_{2}}{d_{1}+d_{2}}]\subset\mathbb{R}$ is a unit interval with the standard metric $dv^{2}$ and

   (1.3)		$\displaystyle d\underline{\nu}_{\mathbb{I}}$	$\displaystyle=C_{n,d_{1},d_{2}}\cdot\mathscr{V}_{\mathbb{I}}(v)dv,$
   (1.4)		$\displaystyle\mathscr{V}_{\mathbb{I}}(v)$	$\displaystyle=\begin{cases}(\frac{v}{d_{1}}+\frac{1}{d_{1}+d_{2}})^{\frac{n-1}{n+1}},&v\in[-\frac{d_{1}}{d_{1}+d_{2}},0],\\ (-\frac{v}{d_{2}}+\frac{1}{d_{1}+d_{2}})^{\frac{n-1}{n+1}},&v\in[0,\frac{d_{2}}{d_{1}+d_{2}}],\end{cases}$

   for some constant $C_{n,d_{1},d_{2}}>0$.

2. (2)

   There is a continuous surjective map $\mathcal{F}_{t}:X_{t}\rightarrow\mathbb{I}$ with the following properties:

   1. (a)

      (Almost distance preserving) For all $p,q\in X_{t}$,

      (1.5)

      $$\Big||\mathcal{F}_{t}(p)-\mathcal{F}_{t}(q)|-d_{\omega_{CY,t}}(p,q)\Big|<\tau(t),\quad\lim\limits_{t\to 0}\tau(t)=0.$$

   2. (b)

      (Regular fiber) For each $v\in(-\frac{d_{1}}{d_{1}+d_{2}},\frac{d_{2}}{d_{1}+d_{2}})\setminus\{0\}$, the fiber $\mathcal{F}_{t}^{-1}(v)$ is an $S^{1}$-fiber bundle $S^{1}\to\mathcal{F}_{t}^{-1}(v)\xrightarrow{\pr_{v}}D$ with the first Chern class

      (1.6)

      $\displaystyle c_{1}(\mathcal{F}_{t}^{-1}(v))=\begin{cases}c_{1}(\mathcal{O}(d_{2})|_{D}),&v\in(-\frac{d_{1}}{d_{1}+d_{2}},0),\\ c_{1}(\mathcal{O}(-d_{1})|_{D}),&v\in(0,\frac{d_{2}}{d_{1}+d_{2}}).\end{cases}$

   3. (c)

      (Singular fiber and deepest bubble) The fiber $\mathcal{F}_{t}^{-1}(0)$ is a singular $S^{1}$-fibration over $D$ with vanishing circles along $H\subset D$. Suitable rescalings around the vanishing circles on $\mathcal{F}_{t}^{-1}(0)$ converge to the Riemann product $\mathbb{C}_{TN}^{2}\times\mathbb{C}^{n-2}$, where $\mathbb{C}_{TN}^{2}$ is the Taub-NUT space.

   4. (d)

      (End bubble) Suitable rescalings around the ends $v_{-}=-\frac{d_{1}}{d_{1}+d_{2}}$ and $v_{+}=\frac{d_{2}}{d_{1}+d_{2}}$ converge to the complete Tian-Yau metrics $\omega_{TY,1}$ and $\omega_{TY,2}$ on $Y_{1}\setminus D$ and $Y_{2}\setminus D$ respectively.